Pitch Estimation via Precomputed Lookup Tables

The patent applies preliminary action by pre-calculating and storing values of the function g(γ) = exp(-γ²/2σ²) in a lookup table before the main estimation process. This precomputation stores frequently needed exponential values that would otherwise require repeated calculation during the EM algorithm iterations, significantly reducing the computational burden while maintaining estimation accuracy.

The patent transforms the continuous frequency domain into a discrete domain by introducing a discretization parameter δf. The continuous probability density function is converted into a discrete representation where frequencies are sampled at intervals of δf. This parameter change from continuous to discrete domain enables efficient computation using digital signal processing techniques while preserving the essential characteristics of the pitch estimation.

The patent creates a universal pitch estimation method that works for any sound mixture regardless of the number of sound sources or presence of fundamental frequency components. The method uses a mixture model that can represent any combination of harmonic and non-harmonic sounds through the probability density function p(f; θ), where θ includes fundamental frequencies, amplitudes, and spectral shapes. This universal approach eliminates the need for assumptions about sound source characteristics.

The patent introduces an intermediary statistical model (mixture distribution model) that bridges the gap between observed frequency components and underlying sound sources. Instead of directly tracing frequency components or assuming fundamental frequencies exist, the method uses probability density functions as intermediaries to represent and analyze the sound mixture, enabling handling of complex overlapping scenarios.

The patent applies preliminary action by pre-computing and storing the function g(γ) values in a lookup table. During the EM algorithm iterations with multiple tone models, instead of calculating exp(-γ²/2σ²) repeatedly, the system retrieves precomputed values from the table, reducing computational overhead while maintaining the accuracy benefits of multiple tone models.

The patent uses approximation by copying precomputed values from the lookup table rather than performing exact calculations each time. The discrete sampling of the probability density function at frequency intervals δf creates a copied representation that approximates the continuous function, enabling efficient computation with multiple tone models while preserving essential accuracy.